## The outer oblique boundary problem of potential theory

• In this article we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients and inhomogeneities. Main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in [1]. Moreover we prove regularisation results for the weak solutions of both, the inner and the outer problem. We investigate the non-admissible direction for the oblique vector field, state results with stochastic inhomogeneities and provide a Ritz-Galerkinm approximation. The results are applicable to problems from Geomathematics, see e.g. [2] and [3].

Author: Thomas Raskop, Martin Grothaus urn:nbn:de:hbz:386-kluedo-16098 Schriften zur Funktionalanalysis und Geomathematik (43) Preprint English 2009 2009 Technische Universität Kaiserslautern 2009/07/13 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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